KöMaL 2013 K400

Steve and Kate are running around the football field, and measuring their times. Steve's stopwatch is set to lap times, that is, whenever he presses the button the watch will store the actual time reading and start the measurement from zero again. Kate's stopwatch is set differently: whenever she presses the button, the watch stores the actual time reading, but it will then continue the measurement without resetting zero. The two of them ran four laps together. Unfortunately, Kate forgot to press the button at the ends of the first and third laps. Thus she only had two readings at the end: 164 seconds and 340 seconds. Based on his own watch, Steve told her that they had run the first lap 5 seconds faster than the mean of the four lap times, and that the mean of the second and third lap times was 4 seconds more than the fourth lap time. How long did they take to cover the fourth lap?